1. ESRF impedance simulation challenges Simon White, Vincent Serrière

2. OBJECTIVES Page 2 Design, procurement, preassembly, construction and commissioning of a new low emittance storage ring to reduce the horizontal equilibrium emittance from 4 nm down to 150 pm Re-use the same tunnel and infrastructure Maintain the existing insertion device and bending magnets beamlines Preserve the time structure operation and a multibunch current of 200 mA Keep the present injector complex Reuse, as much as possible, existing hardware Minimize the energy lost in synchrotron radiation Minimize operation costs and maintain operation reliability Minimize the impact on User Operations due to the downtime for installation and commissioning [courtesy J.L. Revol]

3. MAIN PARAMETERS Page 3 Lattice parametersPresentNew Lattice typeDBAHMBA Circumference [m]844.390843.979 Beam energy [GeV]6.046.00 Natural emittance [pmrad]4000147 Vertical emittance [pmrad]45 Energy spread [%]0.1060.095 Damping times H/V/L[ms]7/7/3.58.5/13/8.8 Energy loss /turn [MeV]4.882.60 Tunes (H/V)36.44/13.3975.58/27.62 Chromaticity (H/V)-130/-58-100/-84 Momentum compaction1.78 10 -4 0.87 10 -4 Qs5.23 10 -3 3.49 10 -3

4. MAGNETS (IN HOUSE DEVELOPMENT – ID GROUP) Page 4 128 Permanent magnet dipoles longitudinal gradient 0.16  0.65 T, magnetic gap 26 mm 1.8 meters long, 5 modules Hybrid Sm2Co17 / Strontium Ferrite 96 Combined Dipole-Quadrupoles 0.54 T / 34 Tm -1 & 0.43 T / 34 Tm -1 64 Octupoles 51.2 10 3 T/m 3 192 Sextupoles Length 200mm 900-2200 Tm -2 Also used as dipole and skew quad correctors 128 High gradient Quadrupoles 384 Moderate gradient quadrupoles Gradient: 85 T/m Bore radius: 12.5 mm Length: 390/490 mm Power: 1-2 kW Gradient: 51 T/m Bore radius: 15.5 mm Length: 160/300 mm Power: 0.7-1 kW 96 Correctors (H/V) Length 120mm 0.08 T All magnets individually powered

5. VACUUM CHAMBER Page 5 Centre Upstream & downstream ID 50*20 mm 30*13 mm (50*13 under design) (reuse of existing ID chambers) TETM 4.489.33 5.9713.14 7.7016.35 8.2917.15 9.8619.73 11.5720.76 11.8921.36 13.8623.55 15.6723.89 15.8624.07 F cutoff [GHz] TETM 6.0813.76 7.0618.29 8.0621.36 9.0622.63 10.3224.72 12.8724.91 13.6925.70 16.1526.70 17.2728.16 18.4229.30 F cutoff [GHz]

6. HARMONIC CAVITY FOR LIFETIME ENHANCEMENT Page 6 Touscheck dominated lifetime: proportional to bunch length Harmonic RF system for bunch lengthening: 3 rd harmonic system: good compromise between size and lengthening factor Achievable bunch lengthening factor: 2.5 to 3 Superconducting passive cavity: easy to tune and to operate down to low driving currents FillingLifetime 200 mA - 7/8  20 hours 90 mA – 16 bunches  2 hours 40 mA – 4 bunches  1.4 hours for  hor = 150 pm  vert = 5 pm

7. IMPACT OF THE NEW DESIGN ON STABILITY Reduced beam pipe aperture- increased geometric and resistive wall wake fields: Stronger single bunch instabilities: TMCI, head-tail, microwave Stronger resistive wall multi-bunch instabilities Beam / lattice parameters: Smaller synchrotron tune: mode coupling instability at lower currents? Higher charge density (smaller beam size): enhanced ion instability? IBS, Touschek: lifetime, losses Lower  -functions: improved single and multi-bunch impedance effects Geometric impedance requires (in most cases) EM simulations, resistive wall wake fields can be derived analytically We are using CST particle studio for 3d simulations Page 7

8. LAYOUT OF THE NEW MACHINE Page 8 Current machine: 2 aperturesNew machine: 3 apertures 32mm 8mm 20mm 8mm13mm The vertical aperture is reduced while keeping the same material for the vacuum chamber There are twice the number of transitions  -functions are smaller How do these combine into overall impedance effects?

9. SINGLE BUNCH EFFECTS: TUNE SHIFT – RESISTIVE WALL ONLY Page 9 Horizontal Vertical New machineCurrent machine Tune shift from resistive wall only: Reduced threshold in the vertical plane: lower Qs Increased threshold in the horizontal: weaker wake field Challenging operation with high bunch intensity? All dipole chambers are now Aluminium: calculations need update (50% fill factor) Vertical Al in high-  regions (Al in dipoles should be even better)

10. MULTI-BUNCH EFFECTS: RESISTIVE WALL ONLY Page 10 Rise time of the last bunch in the train: Simulations done with HEADTAIL including radiation damping 7/8 filling pattern, 868 bunches, 200mA total current Well below TMCI threshold The chromaticity thresholds for the current machine are consistent with operational data Q’~4-6 In all cases a chromaticity of about 4-6 is sufficient to provide stability – feedback is another alternative

11. RECENT MEASUREMENTS Page 11 Threshold ~0.5mA Threshold ~0.6mA Coupled bunch Instability (resistive wall): - Very useful bunch-by-bunch diagnostic developed by E. Plouviez - Validation with model ongoing Measured coupled bunch modes Vertical single bunch instability threshold: -Full impedance budget: TMCI (Q’=0.0) -New machine, resistive wall only ~ factor 3 higher (assuming Al in dipoles): there is still some margin but geometrical impedance needs to be carefully optimized

12. RF FINGERS – ORIGINAL DESIGN Page 12 Top view Side view Cavity Transition (0.2mm step: not realistic) 3 fingers on the top and bottom – weak shielding in the horizontal plane? Beam going off-center in the cavity: horizontal wake on beam axis There are approximately 250 bellows in the machine, cumulated effects could be important if the design is not well optimized

13. OPTIMIZED DESIGN (T. BROCHARD) Page 13 taper:  =5 o, h=0.7mm 0.3mm step Side view, X=0 steeper transition cavity well shielded 5 fingers on the top and bottom: better horizontal shielding – symmetry restored Done for larger beam pipe: frequency shift of the modes More realistic mechanical constraints: steeper transition (1mm instead of 0.2mm)

14. SMOOTHER TRANSITION Page 14 factor ~6 factor ~2 Ongoing effort with the drafting office to find best compromise between impedance and mechanical constraints Reducing the taper angle to 2 o significantly reduces the impedance of the structure: k loss (5 o ) ≈ 2.0e-2 V/pC k loss (2 o ) ≈ 5.0e-3 V/pC A prototype will be installed during the next shutdown in May: we hope to be able to measure heating

15. FLANGES Page 15 Design 1Design 2 strong trapped modes for design 1 ~beam pipe cut-off Two designs initially proposed by the drafting office About 500 flanges in the new machine Design 2 (similar to present design performs much better than design 1 Again, the structure is not axisymmetric: significant horizontal wake on beam axis X1 Z1 X2 Z2

16. COMPARISON WITH PRESENT MACHINE Page 16 X 2015 Z 2015 X2 Z2 Inserted the present beam pipe profile into the design 2 for comparison: In both cases stainless steel was used as the material Present design almost axisymmetric: very little horizontal wake on beam axis Larger number of modes below cut-off for the new machine Loss factors (3mm bunch length): k loss (2015) ≈ 2.1e-2 V/pC k loss (Upgrade) ≈ 3.3e-2 V/pC Drafting office is considering the possibility of “shielding” these flanges (electrical contacts or conductor joint) ~cut-off present machine ~cut-off new machine

17. CURRENT STATUS Resistive wall: Lower synchrotron tune and smaller beam pipe almost fully compensated by smaller  -functions and change of material (SS->Al) in dipoles So far used analytical expression for elliptical beam pipes: design of the chambers now well advanced, check validity of approximation (from first tests it looks ok) Model validation ongoing with measurements on the running machine Geometrical impedance: ESRF upgrade is a brand new machine, model need to be completely updated For most elements we still don’t have a final design: iterations ongoing with drafting office Main elements we looked at so far: RF cavities: full calculations available, no issues there Button BPMs: preliminary optimization done, detailed calculations ongoing RF fingers: initial design not optimal, significant improvement with increased horizontal shielding, need to optimize transitions Flanges: preliminary estimates indicate small degradation with respect to the present machine, drafting office is considering eventual “shielding” of these flanges To de done: tapers, pumping holes (located in the extrusion: should not be an issue), striplines, collimators, absorbers, etc… Page 17

18. OPEN QUESTIONS The new machine will have an equilibrium bunch length of 3mm: We need to look at high frequencies: large number of mesh Is it ok in some case to simulate longer bunches? For instance to look only at the low frequency components or some information will be lost? In lots of cases not axisymmetric in the horizontal plane: Strong ‘constant’ horizontal wake on beam axis: we try as much as possible to minimize it Impact on stability? Closed orbit? Is it really detrimental? We currently model 3mm rms bunch length: Seems good enough for quick estimates, geometry optimization, relative comparisons Already a lot of meshes: at some point we will need the wake function and first trials with deconvolution not very convincing: any alternatives other than having shorter source, i.e finer mesh? Lots of geometries contain very small features (sub-millimeter): Fingers, transitions, etc..: CST does not seem to like non-uniform mesh Sometimes simulations becomes unstable when grid not is not uniform at open boundaries: so far to could be overcome by adding additional material with fine mesh at the boundaries Page 18

19. OPEN QUESTIONS Simulation of Tapers / direct or indirect method: which one is the more accurate ? No bench measurements at ESRF: is it important to validate simulations ? Page 19 Length of beam tube ?